2. Operations Research (OR)
Overview of the OR Modeling Approach
1. Carefully observing and formulating the problem, gathering all relevant data
- Crucial, because affects relevance of the conclusions (it’s difficult to extract a right answer from the wrong problem)
2. Constructing a mathematical model to abstract the essence of the real problem
- Decision variables: x1, x2, …, xn
- Objective function: P (profit) = 3x1 + 2x2 + … + 5xn
- Constraints: x1 + 3x1x2 + 2x2, ≤ 10 restrictions on the values to decision variables
- Parameters: the constants (namely, the coefficients and right-hand sides) in the constraints and objective function
- Sensitivity analysis: analysis of changes in the solution depending on the values of parameters,
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Testing the model and refine it as needed
- Retrospective test use historical data to determine how well the model and the resulting solution would have performed if they had been used, and using alternative solutions from the model on it predicts the relative effects of alternative courses of actions
6. Prepare for the ongoing application of the model as prescribed by management
- Databases and management information systems may provide up-to-date input for the model each time it is used, in which case interface programs are needed
- Decision support system is installed to help managers use data and models to support (rather than replace) their decision making as needed
7. Implementing the system
- Support of upper management (feedback)
- Training for personnel who will use the system
Introduction to Linear Programming
Graphical method (especially for two decision variables only, but also possible for three)
- feasible region is the region of the graphic where the solutions (considering the constraints) can be, that is, the set of permissible values for the decision variables
Standard Form of the Model
- there are functional constraints (or structural constraints) and non negativity constraints (or non-negativity conditions)
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I found the solution to the Woo’s problem by using the tools I mentioned above. I converted the problems constraints into inequalities and from there I was able to put all of them onto a graph and find the feasible region. Then from the prices given in the problem I was able to make my first profit line, and was able to find out the
Get the most out of the constraint when it is identified, or “exploit” it. The constraint must always be managed in specifically working this part of the process.
A company uses 4 pounds of resource 1 to make each unit of X1 and 3 pounds of resource 1 to make each unit of X2. There are only 150 pounds of resource 1 available. Which of the following constraints reflects the relationship between X1, X2 and resource 1?
16) In an unbalanced transportation problem where total demand exceeds total supply, the demand constraints will typically have "≤" inequalities.
A) if the right-hand side value of the constraint increases by 1 unit, the objective function value will increase by 5 units
Write a constraint to ensure that if machine 4 is used, machine 1 will not be used.
Constraints are everything that influences the rhetoric or context of the writing. I suppose you could argue the exigence is the most important but I believe the constraints are what make the essay or article what it should be. If the exigence is the purpose then the constraints are what controls where the purpose goes and what is written or said by the rhetor and what the audience hears or reads. Constraints aren’t necessarily a bad thing or even limiting, I look at it as more understanding the limits of my audience and the reason for writing and the effect it will have on my audience. For this paper in particular without going into understanding the English language and all that one of my constraints would have been the topic. It would have made no sense to talk about horse pedigree in a paper about metal art so my writing had to stay on topic. Another constraint would be I assumed the readers were at least familiar with the trade so my acronyms were understood. While analyzing the paper I can’t forget to mention the kairos of my
When considering operational constraints we looked at people, location, premises, equipment, money, materials, other related activities and services.
Sensitivity analysis allows a change in one particular variable of simulation. This shows how a project is affected by the change. It shows us what can happen in a project with different input
The objective function, decision variables and constraints are fed into solver to arrive at the optimal solution as shown in the below screenshot
The shadow prices for each of the constraints show how much the objective function would get better or worse by if the right hand side was increased by one unit. For instance if the total number of trucks needed for month 1 increased from 10 to 11, the cost would get better by $2485 or decrease by $2485 (since the shadow price is the negative of the dual price). The positive dual values for the long-term trucks show that using the long-term trucks instead of the short-term trucks actually
The main goal of my Decision Science course is to equip executives or any decision maker with tools to deal with the decision making process. The course provides us with a systematic, coherent approach to help with problem solving.
The first constraint is the maximum meals which would be prepared each night. The decision makers wanted to set a fixed maximum so they can get the right amount of ingredients and not produce any extra waste. The set number has been decided by the decision
Decision Support Systems promote a learning culture in an organization. Employees and managers learn new concepts and more efficient ways of improving the organization, either as a byproduct of the application of DSS or from the direct implementation of DSS as training tools. This learning process is good for the company’s future decision making processes.
The objective function to be minimized i.e, the overall cost function of the generator would be the sum of cost function of each